Indian Institute of Technology,New Delhi, 31 October 2008

Indian Academy of Sciences,74th Annual Meeting, New Delhi

Oct. 31 – Nov. 2, 2008

SOMDATTA SINHACentre for Cellular and Molecular Biology (CSIR)

Hyderabad

A Simple Approach to StudyA Simple Approach to Study

Designs in ComplexDesigns in Complex

Biochemical PathwaysBiochemical Pathways

Symposium on“Complexity & Computation in the Natural Sciences”

(Machta, Complexity, 2006: courtesy NOAA and NASA)

Hurricane approaching Florida

The Spiral Galaxy M51

LIVING SYSTEMS ARE COMPLEX SYSTEMSLIVING SYSTEMS ARE COMPLEX SYSTEMS

Complexity arises from selective and nonlinear interactions offunctionally diverse components to produce a coherent structure/function

gcgtacgtacgtagagtgctagtctagtcgtagcgccgtagtcgatcgtgtgggtagtagctgatatgatgcgaggtaggggataggatagcaacagatgagcggatgctgagtgcagtggcatgcgatgtcgatgatagcggtaggtagacttcgcgcataaagctgcgcgagatgattgcaaagragttagatgagctgatgctagaggtcagtgactgatgatcgatgcatgcatggatgatgcagctgatcgatgtagatgcaataagtcgatgatcgatgatgatgctagatgatagctagatgtgatcgatggtaggtaggatggtaggtaaattgatagatgctagatcgtaggtagtagctagatgcagggataaacacacggaggcgagtgatcggtaccgggctgaggtgttagctaatgatgagtacgtatgaggcaggatgagtgacccgatgaggctagatgcgatggatggatcgatgatcgatgcatggtgatgcgatgctagatgatgtgtgtcagtaagtaagcgatgcggctgctgagagcgtaggcccgagaggagagatgtaggaggaaggtttgatggtagttgtagatgattgtgtagttgtagctgatagtgatgatcgtag …….

Our genome encodes an enormous amount ofinformation about our beings.

our looksour sizehow our bodies workour healthour behaviorswho we are

Information plus regulationbio-complexity

proteins

30 000+genes

complexes

pathways

whole cell

community

organs

biological data

The genomic information andits regulation is organised atmultiple inter-connectedmodular and hierarchicallevels of increasingcomplexity

Bacterium E. coli divide in 20 min

Yeast cell cycle - 90 -120 min

Rapidly dividingmammalian cell cycle ~ 24 hours

Large cells -nerve cells in giraffe’s neck ~ 3 m

(9.7 ft) in length.

Smallest cell -Mycoplasma ~ 10-7 cm diameter

Cell is the basic unit of life

Living systems are made up of cells

– single or multi-cellular

Human RBC(7µm)

Bacteria(E.coli 3µm) Muscle Cell (50µm)

Acetabularia(3cm)

Amoeba (330µm)

Individual cells need to have mechanisms tomonitor their environmental composition.

They need to discern and synchronize their responsesaccording to variations in external and internal

conditions.

To achieve this level of coordination, metabolites andchemical compounds are used by the cell asmessages to know the composition of these

environments.

AND

it requires computation and information transferacross breadth and depth of processes

at all levels of organisation

http://www.expasy.ch/cgi-bin/show_thumbnails.pl

Cellular functions are controlled by networks of biochemical reactions

Cellular behaviour is the emergent property of many biochemical reactionsnetworked through feedback/feed-forward processes

Negative Feedback ensures stability and conservation of energy bydesensitizing the system to perturbations - are naturally selected to be the

most common form of regulation in pathways

Positive Feedback is potentially destabilizing, and primarily employed forexcitable, amplification, and switching processes.

Intricate networks of inter-connected chemicalreactions between molecular species in the cell.

Complex network of biochemical reactions in cells co-ordinate and control cellular functions

two interacting sets

GENETIC REACTIONS

Gene induction,repression,replication,

transcription

METABOLICREACTIONS

Conversion of substratemolecules by enzymes,

enzyme inhibition oractivation

Gene & Transcription FactorGene & Transcription Factornetworksnetworks

Metabolic reactionMetabolic reactionnetworksnetworks

Part of the network of direct transcriptional interactions in the E.coli data set, represented using network motifs

Network Motifs: Simple Building Blocks of Complex Networks. Science, (2002)

http://regulondb.ccg.unam.mx/; byF. Sanchez and E. Diaz

Escherichia coli transcriptional regulatory network for sensing the extra-cellular andintracellular environment

TFs:Green: extracellular sensingBlue: internal sensingPink: sensing intracellular conditions using endogenous signals synthesized inside the cellLight orange: unknown mechanisms to modulate their activities.

Lines: Green-activation; Red-repression;Blue: dual (activation & repression)Loops in the TFs: auto-regulation positive, negative or dual.Yellow: genes do not code for TF productsAbbreviations:S, substrate; E, enzyme and P, product.

Global TFs

Srinivasan & Morowitz, Biological Bulletin, 2008

Core Metabolic Network of reductive chemoautotrophs(bacteria that fix carbon by the reductive TCA cycle)

(Minimal metabolome - 287 metabolites)

How can one do predictive studies of

these complex information processingthese complex information processingunits/pathwaysunits/pathways

&&

understand the role of pathway designs inunderstand the role of pathway designs intheir function ?their function ?

“Multiple steps in every pathway”&

“Regulation - Positive/Negative”

The dynamical consequences of these designs canbe quite opposite in pathway functions.

MODELLING BIOCHEMICAL PATHWAYSThree complementary approaches

Construction & analysis offunctionally related

pathways from large scalegene expression and

protein interaction datausing network theory

Model existing pathways based oninformation derived from –

• Genome sequences

• Protein sequences

• Biochemical & Genetic information

REVERSE ENGINEERING LARGE NETWORKS

FORWARD ENGINEERING

All designs that are not physicallyAll designs that are not physicallyforbidden are realizable,forbidden are realizable,

but not all realizable designs arebut not all realizable designs arefunctionally effectivefunctionally effective

(in relation to context and constraintsof the system and environment).

Synthetic oscillatory circuit;Toggle switch in bacteria;

Amplifiers of gene expression.

‘Rational Network Design’

Artificial genetic and enzymaticnetworks with specific

properties constructed basedon mathematical models

FLOW

of

INFORMATION

Transcription rate - ~ 1,000 nucleotides/minuteTranslation rate - ~ 900 amino acids/minute

Production of the proteinto the binding of dimer -~ 3 min

THE INHERENT DELAY IN THE

TRANSCRIPTION-TRANSLATION PROCESS

Starting from gene expression to cellular function involves a sequence ofreactions over a period of time - a common feature

Question

A generic feature in all intracellular biochemical processes is the timerequired to complete the whole sequence of reactions to yield anyobservable quantity - widespread presence of time delay in biological functions.

Theoretically time delay is known to be a source of instability, and hasbeen attributed to lead to oscillations or transient dynamics in several biological functions.

Negative feedback loops, common in biochemical pathways, are known to provide stability, and withstand considerable variations and random perturbations of biochemical parameters.

(Savageau, 1974; Becskei and Serrano, 2000).

Interaction of these two opposing factors- instability and homeostasis -

are common features in intracellular processes

Effect of these divergent forces in the dynamics of gene expression?

Forward Engineering of gene circuitsForward Engineering of gene circuits(Rational network design)(Rational network design)

Construction of desired network with specific properties predictedfrom mathematical models using knowledge from biochemistry,

molecular biology, and genetics.

“It is obvious from analysis of these [bacterial genetic regulatory]mechanisms that their known elements could be connected into a widevariety of ‘circuits’ endowed with any desired degree of stability”

Boolean/Logical Circuits in Biology :Organisms take decisions based on input signals and give a binary (0/1)

response in some cases.

Jacob & Monod Model of theprokaryotic operon (1961)

Gene APromoter Operator

RNAP

Repressor

Inducer

“ Rational Network Design ” can -

a) engineer new cellular behaviour, and

b) improve understanding of naturally occurring networks.

Genetic Circuit Engineering Paradigm

Design - Simulate - Implement & Test

A basic assumption underlying such ‘synthetic’ biology

The properties of individual genetic components can be used

to understand and quantitatively predict circuit-level

behaviors.

v Designed simple negatively auto-regulated transcriptional modules consisting of a basic regulator and transcriptional repressor - with and without delay in repression - and their controls.

Constructed gene circuits in E. coli.

v Developed mathematical models of a simple negativefeedback pathway based on the design of the negatively auto-regulated gene circuit -

deterministic and stochastic

v Compared the gene expression dynamics with theoretical predictions.

ApproachesApproaches

Designing negatively auto-regulated gene circuits -with and without delay in repression

S1 S2(-)

Basic Circuit

Delay Circuit

S1 S’ S2(-)

The presence of one or more genes (“Delay element”) increase the length ofthe transcript, thereby introducing a delay in establishment of negative

feedback by the repressor in Delay circuit compared to the Basic circuit.

Design of negatively auto-regulated gene circuits

(a) Basic Circuit (TG) (b) Delay (C2TG)

Control Delay circuit (TC2G): Position of repressor same as in TG, but position ofreporter is as in C2TG. This is identical to the Delay circuit (C2TG) in length, number ofcistrons, and position of the Reporter gene, except for the position of the repressor, TetR.

TG: tetR gene and reporter gene(gfp) after the promoter-operator

unit (pLtet-01).

C2TG: two copies of cI gene from λ phagebefore the repressor gene - production of the

repressor is delayed.

Deterministicmodel

gt = total no. of promoters;

α1, α2, α3 = degradation rates

β1, β2 = transcription & translation rates

K1, k2 = promoter-repressor complexreaction rate

τ1, τ2 = time delays on the production of pand f from the common mRNA;

m = mRNA

p = repressor

f = reporter

g = freepromoters

ϕ - degradation products of mRNA,TetR and GFP

Stochastic modelmolecular reactions

(Gillespie,1977;Bratsun et al.,2005)

Basic circuit (circles with dashed lines)Delay circuit (squares with solid lines)

Kinetics of TetR

Kinetics of GFP

Det

erm

inis

tic

mo

del

Sto

chastic m

od

el(average of 100 sim

ulations).

The circuit dynamics is stable in all conditions

considered, but with increasing delay time, the

system shows damped oscillations, and the steady

state is reached with progressively larger excursion

in the phase plane.

Our theoretical analysis predicts that the negatively

auto-regulated pathway, as represented in these

models, can show a transient overshoot in gene

expression and protein production due to the delay

in the kinetics of the repression process.

Basic (circles) and the Delay (triangles) circuits upon induction (25 ng/ml)in four independent experiments.

(a) Normalised fluorescence versus time (minute);

(b) Normalised fluorescence versus growth (OD600).

Error bars (one standard deviation) are for both fluorescence and growth.

Experimental kinetics of GFP

Delay circuit shows a large overshoot in gene expression.

Gene expression in population of E. coli cells

with the gene circuits.

Model prediction

and

Experimental measurements.

Frequency distributions of GFP in cell populations:(a) Basic (TG), and (b) Delay (C2TG) circuits at different time intervals.

Intra-population heterogeneity in gene expressionExperimental: FACS analysis

The population of cells with Delay circuit shows –

(i) A significantly higher fluorescence in time, which later return to lower levels;

(ii) Presence of bimodality in fluorescence distribution; and,

(iii) Broader distribution of fluorescence in cell population - larger heterogeneity ingene expression among the individual cells within a population

Intra-population heterogeneity in gene expressionTheoretical: GFP expression at different time points in model 1000 cells with both

circuits having plasmid copy number variation (50±10, normally distributed)

The population of cells with Delay circuit shows –

(i) A significantly higher fluorescence in time, which later return to lower levels;

(ii) No bimodality in fluorescence distribution; and,

(iii) Broader distribution of fluorescence in cell population - larger heterogeneity ingene expression among the individual cells within a population

Frequency distributions of GFP molecules in cell populations:(a) Basic (TG), and (b) Delay (C2TG) circuits at different time intervals.

Contour plots of GFP fluorescence distribution in cell populations.At 1, 2 and 5 hrs after induction with different inducer concentrations -

(i) 25ng/ml, (ii) 50 ng/ml, and (iii) 75ng/ml, of Doxycyline.

BimodalityTG C2TG

The presence of bimodality in Delay circuit cell populations, induced at 25ng/ml,is a consequence of, but not an inherent property of, the delay element in the

circuit. Removal of this low-expressing fraction of cells by gating shows that C2TGcontinues to have a greater spread than TG.

25ng/ml

50ng/ml

75ng/ml

Common measures of comparing variability (noise) in a system -

Coefficient of Variation CV = (standard deviation/mean)*100 and Fano Factor FF = variance/mean.

Basic (TG - dashed line + circle)

Delay (C2TG-solid line + square)

Inset:

Changes in Fano Factor (FF) forboth the circuits.

• During the time of the build-up of the overshoot (till 90 minutes):

CV of the Delay population > Basic population

• The initial decreasing trend in CV in both the circuits indicates reduction in theintrinsic noise levels with time due to the establishment of the repression.

• Fano Factor shows continuing difference between the two circuits. Delay circuitexhibits greater variability compared to the Basic circuit.

Heterogeneity of gene expression in a population of cells

Experiments

Model Delay and Basic circuits -No significant difference in their CV over time except at an

early time point.

Prediction is not consistent with the experimental results ?

Coefficient of Variation for both Basic (dashed lines) and Delay (solid lines) circuits: a) Experimental populations for inducer concentrations

(25 ng/ml - circles, 75ng/ml - triangles) till 60 min from three experiments;b) Theoretical simulation (Basic: dashed line and Delay: solid line).

This prediction is consistent with experimental results.

The experimental Delay circuit at 75ng/ml induction shows similardifference in CV as is seen in the model circuits.

The hypothesis that delay in repression is the primary factor forinducing increased inter-cellular heterogeneity in gene expression in

a population is shown theoretically and experimentally.

CONCLUSIONS

Robustness of the results

Experimental methodology used involved –

1) Population approach (Fluorimetry) – observations on ~ 109 cells

2) Cell level (FACS) – observation on ~ 104 cells

Theoretical model only highlighting the delay in repression – calculations on ~ 103 cells

(no consideration of real factors, e.g., cell size changes, growth, folding delaysof GFP, nonlinearities involved in degradation, etc)

All three approaches show“Overshoot” and “Heterogeneity” in gene expression

The generic origin of delay in biochemical pathways impliesthat there is a high likelihood that the two properties -

transient overshoot & generation of heterogeneity ingene expression in cell population -play important roles in gene regulation.

• The overshoot allows for gene products being available in large amount for multi-step pathways to function,

• It can also act as a dominant source of large deterministic variability paving way to increase the phenotypic diversity in a population ofcells before the negative regulation sets in.

CONCLUSIONS

Our theoretical and experimental results provide importantclues and give possible rationale for delayed feedbacks to

be such a generic feature in gene organisations in cells.

Development of Gene Circuits

Develop integrated computational infrastructure forComputer Aided Design (CAD) of genetic circuitsSimulation and dynamic analysis

Build increasingly complex genetic circuits using well-characterized parts

The Circuit Engineering Vision

Develop a standard library of interoperable “parts” that correspondsto various control functions (www.parts.mit.edu)

We have the “parts list”

How do these “parts” interact as a “whole”, andhow does this system function to create an organism?

Ultimate goal is to link

behaviour of cells, organisms, and populations

to the information encoded in the genome

“Systems Biology”is about identifying, characterizing, and integrating the

parts-lists of complex biological systemsto find the underlying design and working principles of the

biological computational units

Dr. R. Maithreye

Dr. R. R. Sarkar

Dr. Veena K. Parnaik

Dr. Gopal Pande

Council for Scientific & Industrial Research (CSIR)

Department of Biotechnology

Acknowledgements